The English Chief Justice, Lord Judge (yep, that’s his name), has laid down some interim guidelines on tweeting in court. In short, he suggests that tweeting won’t usually prejudice the administration of justice, so it seems that permission should usually be granted. On the other hand, in some circumstances there may be reason to ban tweeting:

Without being exhaustive, the danger to the administration of justice is likely to be at its most acute in the context of criminal trials e.g., where witnesses who are out of court may be informed of what has already happened in court and so coached or briefed before they then give evidence, or where information posted on, for instance, Twitter about inadmissible evidence may influence members of a jury. However, the danger is not confined to criminal proceedings; in civil and sometimes family proceedings, simultaneous reporting from the courtroom may create pressure on witnesses, distracting or worrying them.